Incompressible Fluid Application

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 Revision as of 14:06, 11 December 2009 (view source)Kazem (Talk | contribs) (→Theory)← Older edit Revision as of 14:06, 11 December 2009 (view source)Kazem (Talk | contribs) (→Theory)Newer edit → Line 17: Line 17: \partial_{t}\mathbf{u}-\nu\Delta\mathbf{u} + \mathbf{u}\cdot\nabla\mathbf{u}+\nabla p = \mathbf{f}  \quad  \text{in}  \quad \Omega,  ]0,T[ \partial_{t}\mathbf{u}-\nu\Delta\mathbf{u} + \mathbf{u}\cdot\nabla\mathbf{u}+\nabla p = \mathbf{f}  \quad  \text{in}  \quad \Omega,  ]0,T[ − \qquad \qquad \qquad \qquad\quad \:\:\,\nabla\cdot\mathbf{\rho\mbox{}u} = 0 \qquad \qquad \qquad \qquad\quad \:\:\,\nabla\cdot\mathbf{\rho\mbox{}u} = 0

General Description

 ADVERTISMENT STYLE no numerical details!!!

Theory

The aim of this application is to solve the well known set of Navier-Stokes equations. The problem suffers from severe locking and/or instability using linear FEM.

Failed to parse (lexing error): \partial_{t}\mathbf{u}-\nu\Delta\mathbf{u} + \mathbf{u}\cdot\nabla\mathbf{u}+\nabla p = \mathbf{f} \quad \text{in} \quad \Omega, ]0,T[ \qquad \qquad \qquad \qquad\quad \:\:\,\nabla\cdot\mathbf{\rho\mbox{}u} = 0

This application solve the the equations.... Mathematical approach to the problems.

Nothing numerical

Insert here all the references to your papers...

\qquad \qquad \qquad \qquad\quad \:\:\,\nabla\cdot\mathbf{\rho\mbox{}u} = 0 \qquad \text{in} \Omega,\qquad t\in ]0,T[

\qquad \qquad \qquad \qquad \qquad\quad\:\,\mathbf{u} = \mathbf{u_{0}} \qquad \text{in} \Omega,\qquad t=0

\qquad \qquad \qquad \qquad \qquad\quad\:\:\:\,\mathbf{u} = \mathbf{0} \qquad \text{in} \Gamma,\qquad t\in ]0,T[

Numerical approach

All numerical details here.

This is a part quite open, depending on the application we are considering.

Every physical problem is solved defining many different ingredients. Try to be quite schematic.